Hick’s Law

I do not put much faith in Hick’s Law. I’ve seen it misapplied and drastically misinterpreted. Its limits, and edge-cases, are not widely known. I am convinced that it is generally not a dominant factor, even when it is relevant. I don’t agree with many design choices it is used to justify. In the past 50 years, exceptions to Hick’s Law have been found.

Hick’s “Law” is simply the observation that the time it takes a person to make a decision is proportional to the information-theoretic entropy of the decision. Put another way reaction-time = a-constant-delay + O(entropy of possible responses) ≤ a-constant-delay + O(log(number of choices)). So it takes longer to decide between more options. But adding an option increases the time sub-linearly (at least with a “few” options) — and adding a likely choice slows down the decision time more then adding a few unlikely choices.

Write it right

Unfortunately, most people do not have a good understanding of what Entropy is in information theory. Interaction designers and programmers should at least understand the concept. Unfortunately they don’t always.

When every option has the same probability of being chosen, entropy is maximized. Recall that lg(N) is the entropy when every one of N options is equally probable. So lg(N) is the maximum possible entropy involved in selecting one of N options. (The minimum possible entropy, 0, occurs if one item is always chosen 100% of the time, or no item is ever chosen.) Owing to it’s simplicity, and attractive (but misleading) similarity to Fitt’s Law,
reaction_time = a + b*lg(N), where a and b are empirically determined positive constants, has become the most common formulation of Hick’s Law.

I am not fond of that formulation.

It implies a connection to Fitt’s Law, when it’s pretty clear to me that none exists. Hick’s Law deals with the cognitive processes of decision-making; but Fitt’s Law deals with the iterative physical action of pointing to an object. The two equations are not related, except that that they appear together in HCI literature, and both model a human completing some task. Logarithms also appear in equations modeling radioactive decay — but have no connection to ether’ Hick’s or Fitt’s law.

Stating Hick’s Law in terms of entropy gives better intuition about the decision-process. It shows that the time to make a decision depends as much on the qualities of the alternatives, as how many of them there are. For example, imagine you’ve just won a new sports-car on a game show — now you have to pick one of several different paint-jobs, and drive it off the set. Your choices are: a classic red, safety-green, neon-pink, or Chartreuse and violet tiger-stripes. Like most people, you will probably choose red, and quickly. Now imagine that the choices are: this elegant silver-blue, or classic red. Even though there are only half as many options, it’s clearly a much harder decision, that will take more time. This contradicts the “reaction-time ~ lg(N)” model, but is clearly explained by the entropy-model, because two equally-likly options have a higher associated entropy then one popular option, and several very unpopular options.

A bad justification for bad ideas

Hick’s law has been used to argue that, “giving a user many choices simultaneously is usually faster than organizing the same choices into hierarchical groups. Making choices from one menu of eight items is faster than is making choices from two menus of four items each.” (The Humaine Interface, page 96). Sometimes this is called the Rule of Large Menus. I strongly disagree with this rule of thumb.

The decision that Hick’s Law models is only made after the user has divined enough relevant options. Hierarchically organizing options makes it easier, and faster, for the user to find relevant options. And this makes the whole process faster. Even when Hick’s Law is applicable, it’s not necessarily dominant. Other factors, such as if the users has to scroll or not, have a far greater impact on how fast, and how ergonomically friendly, completing a task is. But we can have our cake and eat it too.

A hierarchically organized presentation does not mean people will build a a hierarchical mental-model. For example, the word processor I am typing this in has hierarchically-organized menus. The Edit menu has top-level commands, including cut/copy/paste, and a sub-menu called Find that has 6 different commands to search for strings in a document. Each command has a keyboard shortcut, ⌘C for copy, ⌘F to enter a string to search, ⌘G to select the next occurrence of the string, and so on. Any of these shortcuts can be used at any time to initiate any of the commands. When I decide what shortcut to use, I am selecting one shortcut out of all possible shortcuts that I know.

People will string-together multipul commands, making them one action in their head. For example, if a “delete” command is always followed by a confirmation dialog, users will learn to automatically hit enter after hitting delete . So the two actions: “delete” and “confirm delete” become one action “delete and confirm”. (This is why confirmation dialogs are a bad idea). So as long as commands exist to navigate a hierarchy, they can be strung together to make a “flat” command that directly selects an option. A user can use consider all “flattened” commands at the same time.

I am not aware on research into, the limits on Hick’s Law — aka what happens if there are a lot of choices? People simply can’t hold 4 billion choices in their head, yet Hick’s Law tells us that choosing between 4 billion equally-likely options should only be about 30 times slower then choosing between 4. And I just can’t accept that as true. At some point, the number of options exceeds a person’s mental capacity — and I would expect that to affect reaction time. But exactly what this limit is, or if it even matters, is not commonly known.

Whisky. Tango. Foxtrot.

I’ve come across some amazingly … incorrect … takes on Hick’s Law. And that makes me even more skeptical of it’s utility.

Here’s a video of Tony Blauer (self-defense instructor) claiming that hicks law means:

If I add more choices, I slow down response time. And if I add more stimuli, I slow down response time. Exponentially.

Exponential growth is of course the exact opposite of what happens, which is logarithmic growth. Yet according to Hock Hochheim, “Many modern instructors just associate a doubling ratio to Hicks-that is, for every two choices, selection time doubles per added choice.” His rebuttal of that exponentially-wrong take on Hick’s Law is interesting reading, if for no other reason then it shows just how prevalent a bit of bad-science can become in a field. It also touches on the notion that the brain has a “fast-track” for dealing with sudden “fight or flight” situations.

Exceptions

I don’t know enough about research into the amygdala and the brain to give any hard facts. But it is my understanding that current research suggests instinctual responses to danger can occur much faster then deliberate thought. Humanly taping into this stress-response seems difficult though…

Another “I don’t know for sure, but it’s worth keeping an eye on” is muscle memory and sports. Athletes seem to be able to respond to a stimulus (a flying ball, a punch, etc.) with blinding speed and without conscious thought.

A phenomenon that Hick’s Law does not account for is habituation. If there is one option, A, in a menu that is chosen many times in a row, the user can not help but develop an automatic response to select A after clicking on the menu.

Conclusions
Hick’s law is best stated as: “Reaction-time = a-constant-delay + O(entropy of possible responses)”.
Hick’s law has been totally misunderstood, and used to draw some very strange conclusions.

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